Lim x- ∞ 10+4x^5+5x^2 / 4x^2+3x+5=

$\lim_{x\to{\infty}}{\dfrac{4\,x^{5}+5\,x^{2}+10}{4\,x^{2}+3\,x+5}}=\lim_{x\to{\infty}}{\dfrac{\dfrac{5}{x^{3}}+\dfrac{10}{x^{5}}+4}{\dfrac{4}{x^{3}}+\dfrac{3}{x^{4}}+\dfrac{5}{x^{5}}}}=\lim_{x\to{\infty}}{\dfrac{4}{0}}=\infty$